What are the common factors of 18xy and 32xy?

1 Answer
Dec 8, 2016

Answer:

The common factors with integer coefficients are:

#+-1, +-2, +-x, +-2x, +-y, +-2y, +-xy, +-2xy#

Explanation:

The prime factorisations of #18# and #32# are:

#18 = 2*3^2#

#32 = 2^5#

Hence their common positive integer factors are:

#1, 2#

If you include negative integer factors then they have common factors:

#+-1, +-2#

Both #18xy# and #32xy# are multiples of #x# and #y#, so ignoring scalar multipliers, their common polynomial factors are:

#1, x, y, xy#

Putting all of the possible combinations together, all of their polynomial factors with integer coefficients are:

#+-1, +-2, +-x, +-2x, +-y, +-2y, +-xy, +-2xy#

The greatest common factor of #18xy# and #32xy# is #2xy#